Equation 677 Database

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Magma 65b3a0f89858…

magma 65b3a0f89858
Size
705
Isomorphism class hash
65b3a0f898588ab98ccbbb52cedbb6f52d8c38c489fe510e99167dc61264e2bb
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 21:18:03
Display reorder
660,319,343,327,592,303,320,344,590,328,304,591,342,318,329,305,339,315,595,330,306,340,316,593,331,307,341,317,594,332,308,325,349,333,587,309,326,350,334,588,310,324,348,335,589,311,321,345,336,586,312,322,346,337,584,313,323,347,338,585,314,687,688,686,685,226,200,192,414,216,224,201,415,193,217,416,202,225,191,215,203,229,413,188,212,204,227,411,189,213,205,228,412,190,214,232,206,198,420,222,230,207,199,421,223,231,208,197,422,221,235,209,194,419,218,233,210,195,417,219,234,211,196,418,220,703,704,701,702,163,582,567,67,299,161,583,65,568,297,66,581,162,566,298,578,159,63,570,302,579,160,64,571,300,580,158,62,569,301,154,573,565,58,294,152,574,563,56,295,153,572,564,57,296,157,576,561,61,293,155,577,562,59,291,156,575,560,60,292,671,672,670,669,460,435,425,71,451,461,436,72,423,452,73,437,459,424,450,438,463,70,428,447,439,464,68,426,448,440,462,69,427,449,466,441,431,77,457,467,442,429,78,458,465,443,430,79,456,469,444,434,76,453,470,445,432,74,454,468,446,433,75,455,679,680,678,677,88,109,101,176,477,86,107,177,102,478,178,108,87,103,479,105,91,179,100,480,106,89,180,98,481,104,90,181,99,482,83,115,92,182,475,84,113,93,183,476,85,114,94,184,474,82,111,95,185,471,80,112,96,186,472,81,110,97,187,473,692,691,690,689,252,283,261,129,539,253,281,130,262,537,128,282,251,260,538,279,248,132,264,542,280,249,133,265,540,278,250,131,263,541,258,274,267,135,534,259,272,268,136,535,257,273,266,134,536,254,277,270,138,533,255,275,271,139,531,256,276,269,137,532,699,700,698,697,54,25,170,8,39,55,23,9,171,40,10,24,53,172,38,21,50,11,173,42,22,51,12,174,43,20,52,13,175,41,45,31,168,14,37,46,29,169,15,35,44,30,167,16,36,48,27,164,17,33,49,28,165,18,34,47,26,166,19,32,663,664,662,661,617,634,624,362,597,618,632,360,625,598,361,633,619,623,596,637,616,358,620,600,635,614,359,621,601,636,615,357,622,599,608,640,630,353,603,609,638,631,351,604,610,639,629,352,602,611,643,626,356,606,612,641,627,354,607,613,642,628,355,605,682,683,684,681,656,659,658,149,657,649,651,150,650,648,151,655,652,654,653,553,550,148,284,1,646,644,146,645,647,552,549,147,551,7,548,555,286,140,3,546,556,287,141,0,547,554,285,142,2,544,558,289,143,6,545,559,290,144,4,543,557,288,145,5,695,696,693,694,523,496,485,116,516,524,497,117,483,517,118,495,522,484,518,499,519,119,488,515,500,520,120,486,513,498,521,121,487,514,529,502,491,122,507,530,503,489,123,508,528,501,490,124,509,525,505,494,125,510,526,506,492,126,511,527,504,493,127,512,667,668,665,666,403,384,371,239,390,404,385,240,369,391,241,386,402,370,392,383,399,238,374,389,381,400,236,372,387,382,401,237,373,388,409,375,366,245,396,410,376,367,246,397,408,377,368,247,398,405,378,365,244,395,406,379,363,242,393,407,380,364,243,394,675,676,673,674 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#e6bbf558fb3ffab686d395ed44cee4ecb6da0873fc29bc1527bdf36d2fd1603f, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 21:18:04 · history